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Slide 12

Radians are units of angle

An angle in radians = arc length / radius

1 radian is just over 57º

There are 2π = 6.28 radians in a whole circle

Slide 13

Angular speed ω is the angle turned through per second

ω = θ/t = 2π / T

2π = whole circle angle

T = time to complete one revolution

T = 2π/ω = 1/f

f = ω/2π

Slide 14

v = 2π r / T and T = 2π / ω

v = r ω

a = v² / r = centripetal acceleration

a = (r ω)² / r = r ω² is the alternative equation for centripetal acceleration

F = m r ω² is centripetal force

Slide 15

Loop the loop is possible if the track provides part of the cpforce at the top of the loop ( ST )

The rest of the cpforce is provided by the weight of the rider

Slide 16

True lack of weight can only occur at huge distances from any other mass

Apparent weightlessness occurs during freefall where all parts of you body are accelerating at the same rate

Slide 17

This rollercoaster produces accelerations up to 4g (40m/s²)

These astronauts are in freefall

Red Arrows pilots experience up to 9g (90m/s²)

Slide 18

The vertical component of the tension (Tcosθ) supports the weight (mg)

The horizontal component of tension (Tsinθ) provides the centripetal force

Slide 19

Regular vibrations or oscillations repeat the same movement on either side of the equilibrium position f times per second (f is the frequency)

Displacement is the distance from the equilibrium position

Amplitude is the maximum displacement

Period (T) is the time for one cycle or or 1 complete oscillation

Slide 20

2 ways of producing a voltage analogue of the motion of an oscillating system

Slide 21

- Oscillations
- Waves
- Going round in circles
- Centripetal Acceleration
- Centripetal Force
- Examples of Centripetal Force
- Circular Motion Calculations
- Period and Frequency
- Angles in circular motion
- Angular speed
- Force and Acceleration
- Circular Motion under gravity
- Weightlessness
- Weightlessness
- The conical pendulum
- Periodic Motion
- Producing time traces
- Time traces
- Simple Harmonic Motion1
- Circular Motion and SHM

- Solar Thermal Energy
- Solar Energy
- Newton’s Laws of Motion
- Radiation Safety and Operations
- Heat-Energy on the Move
- History of Modern Astronomy
- Geophysical Concepts, Applications and Limitations

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